Evaluate 64^(-3/2)

Problem

64(−3/2)

Solution

1. Apply the negative exponent rule by rewriting the expression as the reciprocal with a positive exponent.

64(−3/2)=1/(64(3/2))

2. Interpret the rational exponent using the rule a(m/n)=(√(n,a))m which means taking the square root of the base first.

1/(64(3/2))=1/((√(,64))3)

3. Evaluate the square root of the base.

√(,64)=8

4. Substitute the root back into the expression.

1/8

5. Calculate the cube of the denominator.

8=512

Final Answer

64(−3/2)=1/512

Want more problems? Check here!